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The paper presents the Petri nets model describing the process of rectangular finite element mesh generation and h adaptation. This is the first step towards the formal analysis of all the parts of the existing graph grammar based parallel adaptive hp-Finite Element Method algorithms expressed by graph grammar productions. The mesh transformations are expressed as composite programmable graph grammar productions. The transitions on Petri nets correspond to the execution of graph grammar productions. The graph grammar based algorithms modeled as a Petri net can be analyzed for deadlocks, starvation or infinite execution. The parallel adaptive algorithms have many applications in the area of numerical simulations of different engineering problems, including material science, heat transfer, wave propagation and other.

Graph Grammar Based Petri Nets Model of Concurrency for Self-adaptive hp-Finite Element Method with Triangular Elements